how to get a mask that only contains the inside of a bowl
True normal channel
Given a similar face distribution, you can spot a difference between the normal of the faces on the concave side and the ones on the convex side.

Just sort them with a math node:

And exclude the ones who are pointing straight up if you want to get rid of the border.

Obiuvsly this trick works only for a simple vase like the one you posted, for any other model I would use vertex paint: